Last updated: 2019-11-08

Checks: 7 0

Knit directory: ebpmf_demo/

This reproducible R Markdown analysis was created with workflowr (version 1.5.0). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.

R Markdown file: up-to-date

Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

Environment: empty

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

Seed: set.seed(20190923)

The command set.seed(20190923) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Session information: recorded

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Cache: none

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

File paths: relative

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Repository version: 884360c

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility. The version displayed above was the version of the Git repository at the time these results were generated.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated: 


Ignored files:
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/

Untracked files:
    Untracked:  Untitled.Rmd
    Untracked:  Untitled.html
    Untracked:  analysis/.ipynb_checkpoints/
    Untracked:  analysis/Experiment_ebpmf_simple.Rmd
    Untracked:  analysis/draft.Rmd
    Untracked:  analysis/ebpm_gamma_mixture_experiment.Rmd
    Untracked:  analysis/ebpmf_demo.Rmd
    Untracked:  analysis/ebpmf_rank1_demo2.Rmd
    Untracked:  analysis/plot_g.Rmd
    Untracked:  analysis/softmax_experiments.ipynb
    Untracked:  code/misc.R
    Untracked:  data/Compare_ebpmf_nmf2_out
    Untracked:  data/Compare_ebpmf_nmf2_out_ver2.Rds
    Untracked:  data/ebpm_fail.Rds
    Untracked:  data/nmf_sparse3_elbo.Rds
    Untracked:  data/nmf_sparse3_loadings.Rds
    Untracked:  data/nmf_sparse3_summary.Rds
    Untracked:  data/nmf_sparse6_fit_ebpmf_re_nsnmf.Rds
    Untracked:  data/nmf_sparse6_fit_pg_from_truth.Rds
    Untracked:  data/nmf_sparse7_data.rds
    Untracked:  data/nmf_sparse7_fit_em.Rds
    Untracked:  data/nmf_sparse7_fit_gamma_mix.Rds
    Untracked:  data/nmf_sparse7_fit_gamma_mix_random.Rds
    Untracked:  data/nmf_sparse7_fit_gamma_mix_uniform_weight.Rds
    Untracked:  data/trash/
    Untracked:  verbose_log_1571583163.21966.txt
    Untracked:  verbose_log_1571583324.71036.txt
    Untracked:  verbose_log_1571583741.94199.txt
    Untracked:  verbose_log_1571588102.40356.txt

Unstaged changes:
    Modified:   analysis/Compare_ebpmf_nmf.Rmd
    Modified:   analysis/Compare_ebvaepm_ebpm.Rmd
    Modified:   analysis/Experiment_ebpmf_rank1.Rmd
    Modified:   analysis/ebpm_demo.Rmd
    Modified:   analysis/nmf_sparse.Rmd
    Modified:   analysis/nmf_sparse2.Rmd
    Modified:   analysis/nmf_sparse3.Rmd
    Modified:   analysis/nmf_sparse6.Rmd
    Modified:   analysis/softmax_experiments.Rmd
    Modified:   data/Compare_ebpmf_nmf2_out.Rds

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.

These are the previous versions of the R Markdown and HTML files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view them.

File Version Author Date Message
Rmd 884360c zihao12 2019-11-08 update vignette ebpm
html 3814bfb zihao12 2019-10-22 Build site.
Rmd 08b9948 zihao12 2019-10-22 add vignette for ebpm point gamma
html 8abb684 zihao12 2019-10-20 Build site.
Rmd 0ac2637 zihao12 2019-10-20 vignette for ebpm

EBPM problem

\[ \begin{align} & x_i \sim Pois(s_i \lambda_i)\\ & \lambda_i \sim g(.)\\ & g \in \mathcal{G} \end{align} \] Our goal is to estimate \(\hat{g}\) (MLE), then compute posterior \(p(\lambda_i | x_i, \hat{g})\). Here I use mixture of exponential as prior family.

See model details and derivations in https://github.com/stephenslab/ebpm/blob/master/derivations/ebpm.pdf

library(ebpm)
set.seed(123)
library(ebpm)
library(ggplot2)
library(gtools)
require(gridExtra)
Loading required package: gridExtra

experiment setup

I simulate data from the mixture of exponential, and compare fitting the poisson mean problem with MLE (\(\hat{\lambda}^{mle}_i = \frac{x_i}{s_i}\)), and ebpm_exponential_mixture with different options.
For ebpm, the options are:
* fit_true_g: use the true \(g\)
* fit_true_scale: use the true mixture components to estimate \(\hat{g}\)
* fit_est_scale: estimate mixture components from data, then estimate \(\hat{g}\)

## simulate data
n = 2000
sim = ebpm::simulate_pois_expmix(n, seed = 123)
hist(sim$x, breaks = 100, xlab = "x", main = "hist for data x")

Version Author Date
3814bfb zihao12 2019-10-22
8abb684 zihao12 2019-10-20 
rmse <- function(x,y){
  return(sqrt(mean((x-y)^2)))
}
methods = c()
ll_gs = c()
rmses = c()
## true
methods = c(methods, "true")
ll_gs = c(ll_gs, sim$ll)
rmses = c(rmses, 0)

## MLE
methods = c(methods, "mle")
ll_gs = c(ll_gs, NA)
rmses = c(rmses, rmse(sim$x/sim$s, sim$lam))


## fit (with known g)
fit = ebpm::ebpm_exponential_mixture(x = sim$x, s = sim$s, g_init = sim$g, fix_g = T)
methods = c(methods, "fit_true_g")
ll_gs = c(ll_gs, fit$log_likelihood)
rmses = c(rmses, rmse(fit$posterior$mean, sim$lam))
rm(fit)

## fit (with known true scale (mixture components))
fit = ebpm::ebpm_exponential_mixture(x = sim$x, s = sim$s, scale = list(shape = sim$g$shape, scale = sim$g$scale))
methods = c(methods, "fit_true_scale")
ll_gs = c(ll_gs, fit$log_likelihood)
rmses = c(rmses, rmse(fit$posterior$mean, sim$lam))
rm(fit)

## fit (estimate scale)
fit = ebpm::ebpm_exponential_mixture(x = sim$x, s = sim$s, scale = "estimate")
methods = c(methods, "fit_est_scale")
ll_gs = c(ll_gs, fit$log_likelihood)
rmses = c(rmses, rmse(fit$posterior$mean, sim$lam))
rm(fit)

data.frame(method = methods, ll_g = ll_gs, rmse = rmses)
          method      ll_g      rmse
1           true -2909.614 0.0000000
2            mle        NA 1.0556360
3     fit_true_g -2909.614 0.7873792
4 fit_true_scale -2909.307 0.7870354
5  fit_est_scale -2911.056 0.7900987

plot the \(\lambda\)s

fit = ebpm::ebpm_exponential_mixture(x = sim$x, s = sim$s, scale = "estimate")
df = data.frame(lam_true = sim$lam,lam_hat_mle = sim$x/sim$s, lam_hat_ebpm = fit$posterior$mean)
ggplot(df)+
  geom_point(aes(x = log(lam_true + 1), y = log(lam_hat_ebpm +1)), color = "blue")+
  geom_abline(slope = 1, intercept = 0)+
  guides(fill = "color")+
  ggtitle("lam_true vs lam_hat_ebpm")

Version Author Date
3814bfb zihao12 2019-10-22
8abb684 zihao12 2019-10-20 
ggplot(df)+
  geom_point(aes(x = log(lam_true + 1), y = log(lam_hat_mle + 1)), color = "blue")+
  geom_abline(slope = 1, intercept = 0)+
  guides(fill = "color")+
  ggtitle("lam_true vs lam_hat_mle")

Version Author Date
3814bfb zihao12 2019-10-22
8abb684 zihao12 2019-10-20 
ggplot(df)+
  geom_point(aes(x = log(lam_hat_mle + 1), y = log(lam_hat_ebpm + 1)), color = "blue")+
  geom_abline(slope = 1, intercept = 0)+
  guides(fill = "color")+
  ggtitle("lam_hat_mle vs lam_hat_ebpm")

Version Author Date
3814bfb zihao12 2019-10-22
8abb684 zihao12 2019-10-20 

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] gridExtra_2.3   gtools_3.8.1    ggplot2_3.2.1   ebpm_0.0.0.9002

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2       compiler_3.5.1   pillar_1.4.2     later_0.8.0     
 [5] git2r_0.26.1     workflowr_1.5.0  tools_3.5.1      digest_0.6.22   
 [9] evaluate_0.14    tibble_2.1.3     gtable_0.3.0     pkgconfig_2.0.3 
[13] rlang_0.4.1      yaml_2.2.0       xfun_0.8         withr_2.1.2     
[17] stringr_1.4.0    dplyr_0.8.1      knitr_1.25       fs_1.3.1        
[21] rprojroot_1.3-2  grid_3.5.1       tidyselect_0.2.5 glue_1.3.1      
[25] R6_2.4.0         rmarkdown_1.13   mixsqp_0.2-3     purrr_0.3.2     
[29] magrittr_1.5     whisker_0.3-2    backports_1.1.5  scales_1.0.0    
[33] promises_1.0.1   htmltools_0.3.6  assertthat_0.2.1 colorspace_1.4-1
[37] httpuv_1.5.1     labeling_0.3     stringi_1.4.3    lazyeval_0.2.2  
[41] munsell_0.5.0    crayon_1.3.4